Exact Maximum Likelihood Estimation of Stationary Vector ARMA Models
| dc.contributor.author | Mauricio Arias, José Alberto | |
| dc.date.accessioned | 2023-06-21T01:37:43Z | |
| dc.date.available | 2023-06-21T01:37:43Z | |
| dc.date.issued | 1993 | |
| dc.description.abstract | The problems of evaluating and maximizing the exact likelihood function of vector ARMA models are considered separately. A new and efficient procedure for evaluating the exact likelihood function is presented. This method puts together a set of useful features which can only be found separately in currently available algorithms. A procedure for maximizing the exact likelihood function, which takes full advantage of the properties offered by the evaluation algorithm, is also considered. Combining these two procedures, a new algorithm for exact maximum likelihood estimation of vector ARMA models is obtained. Comparisons with existing procedures, in terms of both analytical arguments and a numerical example, are given in order to show that the new estimation algorithm performs at least as well as existing ones, and that relevant real situations occur in which it do es better. | |
| dc.description.abstract | En este trabajo se estudian por separado los problemas asociados con la evaluación y la maximización de la función de verosimilitud exacta de modelos ARMA multivariantes. Por un lado, se diseña un nuevo algoritmo para evaluar dicha función eficientemente, que reúne una serie de propiedades que se encuentran por separado en los procedimientos actualmente disponibles. Por otro lado, se propone un mecanismo para maximizar la función de verosimilitud, que aprovecha las ventajas ofrecidas por el algoritmo de evaluación. Combinando ambos procedimientos, se obtiene un nuevo algoritmo de estimación por máxima verosimilitud exacta de modelos ARMA multivariantes, cuyo funcionamiento en la práctica resulta superior, en muchos aspectos, al de otros procedimientos alternativos. | |
| dc.description.faculty | Fac. de Ciencias Económicas y Empresariales | |
| dc.description.faculty | Instituto Complutense de Análisis Económico (ICAE) | |
| dc.description.refereed | TRUE | |
| dc.description.status | unpub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/28778 | |
| dc.identifier.citation | Ansley, C.F. (1979), "An Algorithm for the Exact Likelihood of a Mixed Autoregressive-Moving Average Process," Biometrika, 64, 59-65. Ansley, C.F., and Newbold, P. (1980), "Finite Sample Properties of Estimators for Autoregressive-Moving Average Models," Journal of Econometrics, 13, 159-183. Dennis, J.E., and Schnabel, R.B. (1983), Numerical Methods for Unconstrained Optimization and Nonlinear Ecuations, New Jersey: Prentice-Hall. Hannan, E.J. (1969), "The Identification of Vector Mixed Autoregressive-Moving Average Systems," Biometrika, 56, 223-225. Hall, A.D., and Nicholls, D.F. (1980), "The Evaluation of Exact Maximum Likelihood Estimates for VARMA Models," Journal of Statistical Computation and Simulation, 10, 251-262. Hillmer, S.C., and Tiao, G.C. (1979), "Likelihood Function of Stationary Multiple Autoregressive Moving Average Models," Journal of the American Statistical Association, 74, 652-660. Kohn, R., and Ansley, C.F. (1982), "A Note on Obtaining the Theoretical Autocovariances of an ARMA Process," Journal of Statistical Computation and Simulation, 15, 273-283. Koreisha, S., and Pukkila, T. (1989), "Fast Linear Estimation Methods for Vector Autoregressive Moving Average Models," Journal of Time Series Analysis, 10, 325-339. Liu, L.M., and Hudak, G.B. (1992), Forecasting and Time Series Analysis Using the SCA Statistical System (Vol. 1), DeKalb: Scientific Computing Associates. Ljung, G.M., and Box, G.E.P. (1978), "On a Measure of Lack of Fit in Time Series Models," Biometrika, 65, 297-303. Ljung, G.M., and Box, G.E.P. (1979), "The Likelihood Function of Stationary Autoregressive Moving Average Models," Biometrika, 66, 265-270. Nicholls, D.F., and Hall, A.D. (1979), "The Exact Likelihood Function of Multivariate Autoregressive-Moving Average Models," Biometrika, 66, 259-264. Shea, B.L. (1984), "Maximum Likelihood Estimation of Multivariate ARMA Processes via the Kalman Filter," in Time Series Analysis: Theory and Practice (ed. O.D. Anderson), vol. 5, PP 91-101, Amsterdam: North-Holland. Shea, B.L. (1987), "Estimation of Multivariate Time Series," Journal of Time Series Analysis, 8, 95-109. Shea, B.L. (1989), "Algorithm AS 242. The Exact Likelihood of a Vector Autoregressive-Moving Average Model," Applied Statistics, 38, 161-204. | |
| dc.identifier.relatedurl | https://www.ucm.es/icae | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/64199 | |
| dc.issue.number | 16 | |
| dc.language.iso | eng | |
| dc.page.total | 27 | |
| dc.publication.place | Madrid | |
| dc.publisher | Facultad de Ciencias Económicas y Empresariales. Instituto Complutense de Análisis Económico (ICAE) | |
| dc.relation.ispartofseries | Documentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE) | |
| dc.rights | Atribución-NoComercial-CompartirIgual 3.0 España | |
| dc.rights.accessRights | open access | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-sa/3.0/es/ | |
| dc.subject.keyword | Modelos vector ARMA. | |
| dc.subject.keyword | Vector ARMA models. | |
| dc.subject.ucm | Econometría (Economía) | |
| dc.subject.unesco | 5302 Econometría | |
| dc.title | Exact Maximum Likelihood Estimation of Stationary Vector ARMA Models | |
| dc.type | technical report | |
| dc.volume.number | 1993 | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | e835cf57-9199-43c5-a77c-faea005cd3eb | |
| relation.isAuthorOfPublication.latestForDiscovery | e835cf57-9199-43c5-a77c-faea005cd3eb |
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